Question

Radius of a metal sphere is 4 cm. It is given a charge of 8 µC. The force acting on unit area of its surface is ____________.

Options

• 8.953 x 10² N/m²

• 8.953 x 10³ N/m²

• 0.8953 x 10^-2 N/m²

• 89.53 x 10^-3 N/m²

Answer 1

Radius of a metal sphere is 4 cm. It is given a charge of 8 µC. The force acting on unit area of its surface is 8.953 x 10³ N/m².

Explanation:

`"f" = sigma^2/(2epsilon_0 "k") = "q"^2/(2epsilon_0 "k" ("ds")^2)`

`= "q"^2/(2 epsilon_0  "k" (4 pi "R"^2)^2)       ....(because "ds" = 4 pi  "R"^2)`

`therefore "f" = "q"^2/(32  epsilon  _0 "k" pi^2 "R"^4)`

`therefore "f" = (8 xx 10^-6)^2/(32 xx 8.85 xx 10^-12 xx 1 xx 9.86 xx (4 xx 10^-2)^4)`

`therefore "f" = (64 xx 10^-12)/(7.148 xx 10^5 xx 10^-20)`

`= 8.953 xx 10^3  "N/m"^2`